WASHINGTON — The United States added a solid 171,000 jobs in October, and more than a half-million Americans joined the work force, the latest signs that the uneven economic recovery is gaining strength once again.

In addition, more jobs were added in August and September than believed. But the unemployment rate inched up to 7.9 percent because not all those joining the work force found work, the government said Friday.

The report was the final snapshot of the economy before the presidential election.

“The economy is in a lot better shape than most people believe,” said Joel Naroff, president of Naroff Economic Advisors. “That sets us up for stronger growth next year no matter who is elected on

Tuesday.”

A government survey of households found that 578,000 Americans joined the work force in October, the Labor Department said. Of those, 470,000 found work. The difference is why the unemployment rate rose from 7.8 percent in September.

Home prices are finally rising, and retailers and car companies this week reported stronger sales. Consumer confidence in October reached its highest point in almost five years, and stocks are within reach of record highs.

Big businesses are still cautious, partly because of slowing global demand for their goods. But the report found that they continued to add jobs in greater numbers than they did last spring.

A second government survey, of large companies and government agencies, yielded the 171,000 number. Companies added 184,000 jobs, the most since February, and federal, state and local governments cut 13,000.

The report was compiled before Superstorm Sandy struck the East Coast earlier this week and devastated many businesses. Some economists think the rebuilding in the Northeast will add to construction jobs in the months ahead.

The government also revised its data to show that 84,000 more jobs were added in August and September than previously estimated. August’s job gain was revised to 192,000 from 142,000, and September’s to 148,000 from 114,000.

For the third time since the recovery from the Great Recession began in June 2009, the economy appears to be picking up momentum.

Since July, the economy has created an average of 173,000 jobs a month. That is up from an average of 67,000 a month from April through June.

The pickup in hiring suggests that businesses aren’t as worried as many analysts thought about the package of tax increases and spending cuts known as the “fiscal cliff” that will take effect unless Congress acts by Jan. 1.

Companies have cut back spending on computers, industrial machinery and other heavy equipment in recent months. That was seen by many economists as a sign of concern about the cliff and Europe’s economic deterioration.

But better consumer demand may be encouraging employers to hire more employees anyway. James Marple, an economist at TD Bank, said hiring could take off next year if the fiscal cliff is avoided.

“The fact that businesses are continuing to expand even with huge fiscal uncertainty means that once this cloud lifts, the pace of job creation has lots of room to accelerate,” he said.

One big question is whether consumers will be able to keep spending enough to propel growth. Average hourly wages rose only 1.1 percent in the past 12 months, the slowest annual pace on records dating back to 1965.

But the economy has added 1.6 million jobs in 10 months this year. All those new paychecks mean more demand for goods and services, which should lead to more hiring. The country could enter what economists call a virtuous cycle, an escalating loop of hiring, more spending and still more hiring.

Politically, the report was more neutral. It allowed both President Barack Obama and his Republican opponent, Mitt Romney, political ammunition in the fading days of the campaign.

It allowed Obama to argue that the economy has added jobs for 25 consecutive months, since September 2010, and that the private sector has added jobs for 32 consecutive months, since February 2010.

Campaigning in Hilliard, Ohio, the president said: “We’ve made real progress, but we are here today because we know we’ve got more work to do. Our fight goes on.”

The report allowed the Romney campaign, however, to argue that the unemployment rate will be higher on Election Day than it was on Inauguration Day in January 2009, when it was 7.8 percent.

“I won’t waste any time complaining about my predecessor,” Romney said at a rally in West Allis, Wis. “From Day One, I will go to work to help Americans get back to work.”

Obama will face voters with the highest unemployment rate of any incumbent since Franklin Roosevelt. It was 7.8 when Gerald Ford lost to Jimmy Carter in 1976, and 7.2 percent when Ronald Reagan trounced Walter Mondale in 1984.

The story of what happened to the economy during Obama’s term is, of course, more complicated.

The month Obama took office, the economy lost 818,000 jobs, the worst figure of the Great Recession. During the next 13 months he was in office, the economy lost 4.3 million jobs.

Jobs reports were mixed, with some gains and some losses, for the next seven months. Since the beginning of October 2010, the economy has added 3.9 million jobs. The total for Obama’s time in office is growth of 194,000 jobs.

In addition, the Labor Department said in September that 368,000 jobs were created in the year ending in March but have not been assigned to the month-by-month statistics. Adding those jobs, Obama’s total is 562,000.

The economy lost 13,000 jobs during George W. Bush’s first term and added 1.1 million jobs during his second term. The economy added 11.5 million jobs during Bill Clinton’s first term and 11.2 million during his second.

As Obama and Romney face voters, the economy “is showing incredible resilience in the face of significant challenges,” said Marple, the TD Bank economist.

Tom Porcelli, an economist at RBC Capital Markets, was less enthusiastic. “The economy is not falling off a cliff, but it’s not raging ahead with vigor, either,” he said.

Investors also had a measured response. The yield on the 10-year U.S. Treasury note jumped to 1.78 percent from 1.72 percent, indicating investors were moving money out of bonds and into stocks, then dropped to 1.71 percent.

The Dow Jones industrial average climbed as much as 56 points but closed down 139 points, at 13,093.

The unemployment rate has fallen a full percentage point in the past year. But some of that was because people gave up looking for work, and therefore were no longer counted as unemployed.

That pushed the percentage of Americans working or looking for work to 63.5 percent in August, a 31-year low.

But since then, more Americans have started or resumed their job hunts, and most have found work. The percentage of Americans working or looking for work rose for a second straight month in October to 63.8 percent.

The number of people with part-time jobs who wanted full-time work dropped last month. And the number of people who have stopped looking for work also declined. The so-called underemployment rate, which consists of those two groups plus the unemployed, dipped to 14.6 percent from 14.7 percent.

The government’s breakdown of October job growth showed that the housing market is finally generating jobs. Construction companies added 17,000, the most since January. Manufacturers added 13,000 after shedding 27,000 the previous two months.

Professional services such as architects and computer systems providers also added jobs. So did retailers, hotels and restaurants, and health care.

Vocus Inc., a Beltsville, Md., company that makes marketing software, has ramped up hiring this year to keep up with rapid growth in demand. It has nearly doubled its staff to about 750 and plans to add at least 200 next year.

The company is benefiting as more businesses switch from newspaper ads and the Yellow Pages to social media and online search engines. Vocus expects revenue to jump more than 50 percent this year compared with 2011.

Companies “are still willing to make investments in marketing software,” Rick Rudman, the chief executive, said. “We’re helping people grow their businesses.”

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